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Solution - Linear equations with one unknown

n = - 4

n=-4

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Video Explanation

Watch a video of the solution to 2-1/2n=3n+16

Step-by-step explanation

1. Group all n terms on the left side of the equation

$2 + \frac{- 1}{2} n = 3 n + 16$

Subtract $3 n$ from both sides:

$(2 + \frac{- 1}{2} n) - 3 n = (3 n + 16) - 3 n$

Group like terms:

$(\frac{- 1}{2} n - 3 n) + 2 = (3 n + 16) - 3 n$

Group the coefficients:

$(\frac{- 1}{2} - 3) n + 2 = (3 n + 16) - 3 n$

Convert the integer into a fraction:

$(\frac{- 1}{2} + \frac{- 6}{2}) n + 2 = (3 n + 16) - 3 n$

Combine the fractions:

$\frac{(- 1 - 6)}{2} n + 2 = (3 n + 16) - 3 n$

Combine the numerators:

$\frac{- 7}{2} n + 2 = (3 n + 16) - 3 n$

Group like terms:

$\frac{- 7}{2} n + 2 = (3 n - 3 n) + 16$

Simplify the arithmetic:

$\frac{- 7}{2} n + 2 = 16$

2. Group all constants on the right side of the equation

$\frac{- 7}{2} n + 2 = 16$

Subtract $2$ from both sides:

$(\frac{- 7}{2} n + 2) - 2 = 16 - 2$

Simplify the arithmetic:

$\frac{- 7}{2} n = 16 - 2$

Simplify the arithmetic:

$\frac{- 7}{2} n = 14$

3. Isolate the n

$\frac{- 7}{2} n = 14$

Multiply both sides by inverse fraction $\frac{2}{- 7}$ :

$(\frac{- 7}{2} n) \cdot \frac{2}{- 7} = 14 \cdot \frac{2}{- 7}$

Move the negative sign from the denominator to the numerator:

$\frac{- 7}{2} n \cdot \frac{- 2}{7} = 14 \cdot \frac{2}{- 7}$

Group like terms:

$(\frac{- 7}{2} \cdot \frac{- 2}{7}) n = 14 \cdot \frac{2}{- 7}$

Multiply the coefficients:

$\frac{(- 7 \cdot - 2)}{(2 \cdot 7)} n = 14 \cdot \frac{2}{- 7}$

Simplify the arithmetic:

$1 n = 14 \cdot \frac{2}{- 7}$

$n = 14 \cdot \frac{2}{- 7}$

Move the negative sign from the denominator to the numerator:

$n = 14 \cdot \frac{- 2}{7}$

Multiply the fraction(s):

$n = \frac{(14 \cdot - 2)}{7}$

Simplify the arithmetic:

$n = - 4$

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Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

Terms and topics

Linear equations with one unknown

Solution - Linear equations with one unknown

Video Explanation

Step-by-step explanation

1. Group all n terms on the left side of the equation

2. Group all constants on the right side of the equation

3. Isolate the n

Why learn this

Terms and topics

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